All Kleinian groups of co-finite volume less than or equal to some arbitrary fixed constant are homomorphic images of a finite number among them. In fact, their quotients arise from generalized Dehn surgery on finitely many hyperbolic 3-orbifolds of volumes with the same bound. This result goes back more than a decade and appeared, in the torsion-free case, in Thurston’s (unpublished) lecture notes. A result of Craig Hodgson’s is used to show that the hyperbolic 3-orbifolds of bounded volume may be well-ordered, essentially by their volumes.